Wigner representation of Andreev-reflected charge pulses

Recent experiments have shown that the edge states of a quantum Hall sample can be coupled to a superconductor, so that incoming electrons can be Andreev converted by the superconductor as coherent superpositions of an electron and a hole. In parallel, single-electron emitters that operate in the gigahertz regime have been realized in circuits based on quantum Hall edge states. Motivated by this remarkable experimental progress, we analyze here the Andreev reflections of incoming charge pulses on the interface with a superconductor. To this end, we employ a Wigner function representation that allows us to visualize the response function of the interface in both the time and frequency domains. We analyze the response of an interface between a normal metal and a singlet or triplet superconductor with and without an insulating barrier between them. As a special case, we analyze the Andreev reflections of clean single-particle excitations that are generated by the application of Lorentzian-shaped voltage pulses to the contacts of the inputs. Our predictions may be tested in future experiments with edge states coupled to superconductors.